A. Field of the Invention
This invention relates to monitoring the power flowing through electric power transmission lines. More particularly, the invention relates to a method and system for selecting positions for a preferred placement of a plurality of magnetic field monitors where a change in the power flowing through the transmission line will result in a maximum change in the magnetic field at the positions.
B. Description of Related Art
Information about the power flowing through electric power transmission lines and electric power generation facility output is useful and valuable for companies engaged in the business of buying and selling electric power on the open market. Electric power producers do not currently release this information to other participants in the market.
A typical overhead transmission line consists of three conductor bundles, separated from each other in a spatial configuration and running between transmission line towers. Each conductor bundle carries a different phase of the power transmitted through the line, and the total power flowing through the transmission line is the summation of the power flowing through each of the three conductor bundles. Conductor bundles typically consist of 2 to 4 conductors in a bundle. For convenience, conductor bundles will be referred to hereinafter as “conductors,” which shall be understood to refer to the medium of a transmission line that carries the phases of the power flowing through the transmission line. The conductors making up each transmission line carry alternating current (AC) at a specific frequency (60 Hz in the United States, 50 Hz in Europe). The currents flowing in a transmission line generate magnetic fields and the high voltages (typically ranging from 12 kV to 1,000 kV) generate electric fields. The net electric and magnetic fields that surround a transmission line are a superposition of the fields created by the currents and voltages associated with each individual conductor. Both the electric and magnetic fields are largest close to the conductors and fall off rapidly with distance from the conductors.
Often, the transmission line towers will carry several transmission lines, which will be referred to herein as a “line set” or a “transmission line set”. For convenience, the terms “line set” and “transmission line set” will be understood to also include configurations where only a single transmission line is present. The net electric and magnetic fields that surround the transmission line set are a superposition of the fields created by the individual conductors of each transmission line. Each transmission line may carry a power flow that differs in magnitude and direction from any other transmission line in the transmission line set. For example, a transmission line set may have a first transmission line carrying 100 megawatts (MW) in one direction, and a second transmission line carrying 300 MW in the opposite direction.
The “conductor configuration” is the actual, geometric arrangement of the conductors in the transmission line set. Several exemplary configurations are shown in FIG. 1a-FIG. 1f, including: vertical parallel (FIG. 1a); horizontal parallel (FIG. 1b); triangular parallel (FIG. 1c); vertical single (FIG. 1d); horizontal single (FIG. 1e); and triangular single (FIG. 1f). The general spatial configuration of the transmission line set (e.g. vertical parallel, horizontal parallel, triangular parallel, etc.) will most likely be consistent along large spans of the transmission line set. However, the actual geometric arrangement of the lines will vary from transverse area to transverse area along the line as a result of variations in the tension and sag in the individual conductors. Additionally, individual conductor sag will also affect the distances of the individual lines from the ground continuously along the transmission line set.
Transmission line sets are designed to operate at fixed voltage values and a maximum power/current capacity. These values can be obtained from available power line mapping resources (such as Platts Power Map, of Platts, Colo.).
The relationships between the currents and voltages associated with the transmission line set and the resulting electric and magnetic fields are characterized by well-known mathematical models (primarily Maxwell's Law and the Biot-Savart Law). Thus, the electric and magnetic fields contain the information necessary to determine the currents and voltages (i.e. power) that produced them. U.S. Pat. No. 6,771,058, incorporated herein by reference, describes an apparatus and method for the measurement and monitoring of electrical power flowing over a high-voltage electric power transmission line set, including a method of determining the power flowing through a transmission line set from measured electric and magnetic field data.
The amount of power flowing through a transmission line set is determined by the current times the voltage as shown in equation (1).
                              Power          ⁡                      (            MW            )                          =                              V            L                    ⁢                                    ∑              i                        ⁢                                          I                i                            ⁢              cos              ⁢                                                          ⁢              ϕ                                                          (        1        )            where VL is the line voltage,
      ∑    i    ⁢      I    i  is the summation of the currents through each conductor, and φ is the difference between the phase of the line voltage and phase of the line current. Because the voltage of a transmission line set is fixed, the amount of power flowing through that line at any particular time can be measured by determining the current through the line. The current produces the aforementioned magnetic field, the measured magnitude of which, when analyzed in light of the conductor configuration and the distance of the measuring point from each of the conductors, determines the amount of power through the line.
The magnetic field associated with an overhead transmission line set is generally considered in terms of the magnetic flux density vector, B, in Tesla surrounding the lines, which is directly proportional to the conductor currents Ii as shown in equation (2) and inversely proportional to the distance ri from the center of the each conductor to the point of measurement.
                    B        ∝                              ∑            i                    ⁢                                    I              i                                      r              i                                                          (        2        )            The magnetic flux density vector, B, lies along the XY plane perpendicular or transverse to the length axis (Z) of the conductors and points according to the “right-hand-rule” either clockwise or anti-clockwise dependent on the direction of current flow. This vector can be resolved into horizontal and vertical components Bx and By, respectively. As used herein, the term “magnetic field” refers to the magnetic flux density vector, including but not limited to the magnitude and orientation of the magnetic field and its components.
The phase relationship between the current and voltage on the line determines the power factor (or more generally, the direction of power flow). This phase relationship is translated to the phases of the resulting magnetic and electric fields, so the phase relationship of these fields at any measuring point can be used to determine the direction of flow, once similarly adjusted for the line geometry and other factors. Thus, it is possible to determine the amount and direction of power flowing through a transmission line set (the “power flow” of the transmission line set) by measuring the electric and magnetic fields associated with the line set and processing the information appropriately. (See: U.S. Pat. No. 6,771,058.)
In practice, errors in power determination arise due to imperfections in the measurement equipment and inaccuracy of various assumptions used in the mathematical models described in equations (1) and (2). The first group includes imperfect sensor alignment and orientation with respect to the magnetic and electric fields. An additional source of error involves less than perfect sensor calibration. Calibration errors stem from the assumptions made in the mathematical model. The distances between the conductors and the sensing equipment are assumed to be fixed. However, the amount of sag on the lines as a result of temperature induced linear expansion means these distances are variable. In applying equation (2) the measured magnetic field is modeled to be a result of equal current flowing in each conductor bundle associated with the line. In reality, small current imbalances exist between the conductor bundles. These imbalances cannot be measured directly, but will lead to distortion in the magnetic field measurements that are difficult to account for in the magnetic field model. In addition, the model does not take into consideration any external currents induced through the ground wire and other related tower structures. These currents will result in distortions in the measured magnetic field and are very difficult to include in the model. The extent of measurement and model inaccuracies vary with the amount and distribution of power flowing through a particular transmission line set and the complexity of the conductor configuration.
Additionally, the resultant fields created by the conductor configuration and power flow of a transmission line set vary when the amount of power flowing through the transmission line set varies. Accurate monitoring of the power flow through the transmission line set requires accurate detection of changes in the resultant fields. For instance, a vertical parallel conductor configuration, such as that shown in FIG. 1a, may produce a horizontal magnetic field sectional view for various power flows as shown in FIG. 2. In certain areas 202, 204 large changes in power flow result in only minimal changes in magnetic field. Combined with the intrinsic measurement errors discussed above, placing magnetic field monitors in these areas will likely result in difficulty in accurately detecting changes in power flow. However, in another area 206 changes in power flow result in large changes in magnetic field, such that intrinsic measurement errors are unlikely to affect accurately detecting changes in power flow. Therefore, it is preferable to place magnetic field sensors at positions where minimal changes in power flow through the line results in a maximum change in the magnetic field.
Thus, there is a need for a method and system for monitoring the power flowing through an electric power transmission line set using magnetic field monitors placed at selected positions where a predetermined change in the power flow of the transmission line set results in a maximum change in the magnetic field at the positions. Additionally, there is a further need for a method for selecting the positions for the preferred placement for such magnetic field monitors.